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TZID:Asia/Jerusalem
BEGIN:STANDARD
DTSTART:20151025T020000
TZOFFSETFROM:+0300
TZOFFSETTO:+0200
TZNAME:IST
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DTSTART:20160325T020000
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UID:calendar.44834.field_date.0@mathematics.huji.ac.il
DTSTAMP:20200710T110613Z
CREATED:20171116T060001Z
DESCRIPTION:Date: \n\n2:00pm to 3:00pm\n\n\n\n\nSee also: Dynamical & Pro
bability\, Events & Seminars\, Seminars\, Dynamical & Probability\, Events
& Seminars\, Seminars\, Dynamical & ProbabilityLocation: \n\nManchester b
uilding\, Hebrew University of Jerusalem\, (Room 209)\n\n\nTitle: Self-aff
ine measures with equal Hausdorff and Lyapunov dimensions\n\nAbstract:\nLe
t μ be the stationary measure on ℝd which corresponds to a self-affine ite
rated function system Φ and a probability vector p. Denote by A⊂Gl(d\,ℝ) t
he linear parts of Φ. Assuming the members of A contract by more than 12\,
it follows from a result by Jordan\, Pollicott and Simon\, that if the tr
anslations of Φ are drawn according to the Lebesgue measure\, then dimHμ=m
in{D\,d} almost surely. Here D is the Lyapunov dimension\, which is an exp
licit constant defined in terms of A and p.\n\nI will present a new result
which provides general conditions for μ to be exact dimensional with dimμ
=D\, whenever Φ satisfies strong separation. These conditions involve a lo
wer bound on the dimension of the Furstenberg measure corresponding to A a
nd p. The proof uses random matrix theory\, and upper bounds on the dimens
ion of exceptional sets of sections and projections of measures.\n\nBy usi
ng this I will present new explicit examples of self-affine measures whose
dimension can be computed. These examples rely on new results by Hochman
and Solomyak\, Bourgain\, and Benoist and Quint\, regarding the Furstenber
g measure.\n\n Export\n \n\n \nsubscribe iCal
DTSTART;TZID=Asia/Jerusalem:20151110T140000
DTEND;TZID=Asia/Jerusalem:20151110T150000
LAST-MODIFIED:20171228T140836Z
SUMMARY:Dynamics & probability: Ariel Rapaport (HUJI) ' Self-affine measure
s with equal Hausdorff and Lyapunov dimensions'
URL;TYPE=URI:https://mathematics.huji.ac.il/event/dynamics-probability-arie
l-rapaport-huji-self-affine-measures-equal-hausdorff-and-lyapunov
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